Test the Indicated Claim About the Means of Two Populations

question 87

Essay

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations
are equal. Use the traditional method or P-value method as indicated.
-A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars).
$$\begin{array} { c | r r } \text { Female } & \text { Male } & \\\hline 495 & 722 & 518 \\760 & 562 & 904 \\556 & 880 & 1150 \\904 & 520 & 805 \\520 & 500 & 480 \\1005 & 1250 & 970 \\743 & 750 & 605 \\660 & 1640 &\end{array}$$
Use a 0.05 significance level to test the claim that the mean salary of female employees is less than the mean salary of male employees. Use the traditional method of hypothesis testing. $$\text { (Note: } \left. \overline { \mathrm { x } } _ { 1 } = \$ 705.375 , \overline { \mathrm { x } } _ { 2 } = \$ 817.067 , \mathrm {~s} _ { 1 } = \$ 183.855 , \mathrm {~s} _ { 2 } = \$ 330.146 . \right)$$

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Definitions:

F Distribution

A continuous probability distribution that arises frequently as the null distribution of a test statistic, especially in the analysis of variance (ANOVA).

Numerator

The top number in a fraction, representing the part of the whole or the dividend in division.

Chi-square Distribution

A statistical distribution that describes the distribution of the sum of the squares of a set of variables, often used in hypothesis testing.

Random Variable

A variable that can take on numerical values based on the outcomes of a random event.